For puzzles whose entire permutation space is semantically similar enough, your claim is likely true. But for puzzles whose permutations can involve more "human" semantic manipulations, there is likely a much higher risk of failure.
If you mean to say that the permutations of the puzzle extend to changing the rules such as "if it's the Sabbath then reptiles can't travel" then sure it would require more representative examples and may never meet your standard of "error free" but I would also argue the same applies to humans when you present them a logic puzzle that is new to them.
No, but you would need "enough"; whatever that number happens to be.
> It would only need a few descriptions of each animal plus a few examples of the puzzle to understand the logic.
That's the mistake.
GPT itself can't combine those two things. That work has to be done by the content of the already-written training corpus.
And the result is not the same as "understanding logic". It doesn't model the meaning of the puzzle: it models the structure of examples.
GPT can't distinguish the meaning of rules. It can only follow examples. It can't invent new strategies, it can only construct new collections of strategy parts; and it can only pick the parts that seem closest, and put those parts into a familiar order.
GPT doesn't play games, it plays plays.